JEE Main 2016MathematicsHeights and DistancesEasyMCQ

JEE Main 2016 — Heights and Distances Question with Solution

JEE Main 2016 (10 Apr Online)

Question

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o . The angle of elevation of the top of the same tower from a point B, due south of A is 30o . If the distance between A and B is 542m , then the height of the tower (in meters), is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D54

Step-by-step explanation

Let height of the tower be 'H' 
 Let AP=x
BP=y
In ∆APQ⇒tan⁡45o=Hx ⇒  H=x
In ∆BPQ⇒tan⁡30o=Hy  ⇒  y= 3 H

Since,  ∆APB is a right-angled triangle.
⇒x2+5422=y2     (Pythagoras Theorem )
⇒H2+5422=3H2
⇒5422=2H2
⇒542= 2H
⇒54=H

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About this question

This is a previous-year question from JEE Main 2016, covering the Heights and Distances chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.